The two main moons in the Kingdom of Loathing are named Ronald and Grimace. They can be visited (and could be seen from The LAAAAME Observatory, while it lasted), and their phases affect several things in the Kingdom. There are certain days, called Stat Days, on which stat gains are 25% higher for one particular stat if not in Hardcore or Ronin. If Ronald is full, MP gains from resting or relaxing are doubled. If Grimace is full, HP gains from resting are doubled. Other things vary with the amount of moonlight available.

The revolutions of Ronald determine the length of a KoL month in the KoL Year. Ronald takes one KoL month to complete one revolution, while Grimace completes its revolution once every two KoL months. A mini-moon called Hamburglar, a former chunk of Grimace, is in orbit around both, through 11 positions, advancing two positions every day. It adds or subtracts light, affecting the effects of moon-dependent equipment, but not changing stat days. The whole cycle repeats once every 176 days (about half a real-life year).

Most moon-dependent equipment works off the total amount of light coming from the moons. The formula for this is as follows:

Count one for every lit sector of Ronald and Grimace (0 for a new moon, 4 for a full moon).

If Hamburglar is in front of a lit sector it will be dark and block the light -- subtract 1.

If it's in front of a dark sector it will be lit -- add 1.

If it's to one side of either moon then it is lit if the neighboring sector is lit -- adding 1 if it's lit, but having no effect if it's dark.

In the front and center position, it is lit if either the right side of Ronald or the left side of Grimace is lit -- and if both are, it has a doubled effect, adding 2.

When it's behind a moon it has no effect.

Adding all these together you get a number from 0 to 8, which represents the amount of light from the moons.

Out of the moons' cycle of 176 days, they give an average of 4.27 units of light, giving the following distribution of days at varying degrees of light throughout the cycle:

Degree of light

0

1

2

3

4

5

6

7

8

Number of days

8

12

12

19

33

42

34

15

1

To give a sense of just how the 16 day/11 day cycle plays out, here's a graphical representation of the light fluctuations over the full 176 day cycle.

Grimacite Equipment

The Grimacite equipment has a different formula. Being previously a part of Grimace, it is particularly attuned to its motions, but less so for Ronald. Hamburglar, as it was also once part of Grimace, also has an effect. For them, count one for each dark segment of Grimace (unless it's blocked by lit Hamburglar), plus one if Hamburglar is visible and dark.

Out of the moons' cycle of 176 days, the average darkness is 2.2954 units of light, giving the following distribution of days at varying degrees of light throughout the cycle:

Darkness level

0

1

2

3

4

5

Number of days

18

34

46

44

24

10

A graphical representation of the darkness level fluctuations over the full 176 day cycle:

While not Grimacite items, the Periodical Paintbrush and Seasonal Beret are special items whose enchantment also depends on the darkness of Grimace and Hamburglar, with +5% to each attribute for each darkness unit.

For a rundown of upcoming moons see Noblesse Oblige's or Coldfront's calendar. You can also enter chat and give a private message consisting of "day" to Chatbot (/msg chatbot day) to be told how many days until the moons have an effect on a stat.

References

The names of the moons, Ronald and Grimace, are the same as Ronald McDonald and the Grimace, two of the mascots of the McDonald's fast-food restaurant chain. Also, the mini-moon orbiting both larger moons was officially named Hamburglar by the Dev team, the name of another mascot of the chain.

As for the moons themselves, they are very reminiscent of Trammel and Felucca, the moons from the Ultima series of games by Richard Garriott.